1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi- cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as...